Using the membrane model which is based on the brick-wall model, we have calculated the free energy and entropy of the Vaidya-Bonner black hole due to fermion fields. The result shows that the entropy of the Vaidya-Bonner black hole is exactly proportional to the area of its event horizon. The relationship between the entropy and event horizon in such a non-static case is just the same as that in a static or stationary cases.